Sources told ESPN that Barca were nearing a €55 million ($62m) deal for Torres, with the move now completed.
Manchester City director of football Txiki Begiristain said: "Ferran should be proud of what he has achieved here at Manchester City.
"Last season was his first time in a new country, but he adapted well. He always gave 100%, worked hard for the team and scored goals which helped us win trophies.
"Injury unfortunately prevented him from playing more games this season, but Ferran is a player we have all enjoyed working with and we wish him all the best at Barcelona and for the rest of his career."
Torres, 21, has signed a contract at Camp Nou until 2027 with a €1 billion release clause and could make his debut in the Copa del Rey against Linares Deportivo on Jan. 5 -- he won't be registered in time to face Mallorca on Jan. 2 -- having recovered from a foot injury that's kept him out since September.
Barcelona's financial problems have been well documented, with gross debts of over €1 billion leading to the exits of Lionel Messi and Antoine Griezmann last summer.
However, club sources told ESPN they don't envisage any problems inscribing Torres with LaLiga when the registration window opens on Jan. 3.
The club must also register Dani Alves, but the departure of Griezmann at the end of August and Sergio Aguero's retirement due to a heart condition have given them some room to manoeuvre inside their LaLiga-imposed €97m spending limit for the season -- the limit includes salaries and money spent on signings, but fees are broken down over the length of the contract.
Barca are permitted by the Spanish league to spend 25% of whatever they save in wages or by bringing in transfer fees.
The club continue to work on making more room and sources add they hope to do so by ending the loans of Yusuf Demir and Luuk de Jong early and are open to offers for several other players.
Penning Ousmane Dembele down to a new contract would also help, as it would spread the amortisation payments for his fee over a longer length of time.
Torres becomes the second Barca signing under head coach Xavi Hernandez, following the arrival of Alves on a free transfer in November.
ESPN reported in November that Barca had stepped up their efforts to sign Torres, a player they have held a long-standing interest in, and the 21-year-old informed City boss Pep Guardiola of his desire to leave last week.
When asked about Torres' imminent exit from the Premier League, Guardiola said he did not want to keep a player who wanted to play elsewhere.
"I want the happiness of my players. I said many times, if you are not happy, you have to leave. We are not a club like other clubs, the guys who want to leave have to leave," Guardiola said.
Torres scored 16 goals in 43 appearances for City since joining in a €23m ($26m) in August 2020. He has 12 goals in 22 caps for Spain.